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Neural Networks (NNs) can be used to solve Ordinary and Partial Differential Equations (ODEs and PDEs) by redefining the question as an optimization problem. The objective function to be optimized is the sum of the squares of the PDE to be solved and of the initial/boundary conditions. A feed forward NN is trained to minimise this loss function evaluated on a set of collocation points sampled from the domain where the problem is defined. A compact and smooth solution, that only depends on the weights of the trained NN, is then obtained. This approach is often referred to as PINN, from Physics Informed Neural Network~\cite{raissi2017physics_1, raissi2017physics_2}. Despite the success of the PINN approach in solving various classes of PDEs, an implementation of this idea that is capable of solving a large class of ODEs and PDEs with good accuracy and without the need to finely tune the hyperparameters of the network, is not available yet. In this paper, we introduce a new implementation of this concept - called dNNsolve - that makes use of dual Neural Networks to solve ODEs/PDEs. These include: i) sine and sigmoidal activation functions, that provide a more efficient basis to capture both secular and periodic patterns in the solutions; ii) a newly designed architecture, that makes it easy for the the NN to approximate the solution using the basis functions mentioned above. We show that dNNsolve is capable of solving a broad range of ODEs/PDEs in 1, 2 and 3 spacetime dimensions, without the need of hyperparameter fine-tuning.

Migraine appears to be the most common neurological syndrome in primary care. Pain in migraine is mediated by the release of inflammatory mediators at the level of nerves and blood vessels. The antioxidant and neuroprotective effects of vitamin D in the central nervous system suggest that deficiency of this vitamin can be involved in migraine. Moreover, low serum levels of vitamin D correlates with a higher incidence of chronic pain, including migraine and in co-administered with anti-migraine treatment reduces the frequency of migraine attacks. We report a 46-year old woman affected by migraine, anxiety and mild depressive mood (MSQ score: 24; BDI score: 34; VAS score: 8) that partially improved with pregabalin treatment (VAS: 5). Laboratory findings documented low serum levels of vitamin D (25-hydroxy-vitamin D: 12 ng/mL; normal range: 20–100 ng/mL; 1-25 di-hydroxy-vitamin D: 19 ng/mL, normal range: 25–66 ng/mL). The treatment with 10,000 UI vitamin D during pregabalin therapy induced an improvement of clinical symptoms (pain, anxiety and depression) and of the quality of life. This case report suggest that in chronic migraine patient with anxiety and mild mood depression in treatment with pregabalin a supplementation of vitamin D improvement the clinical symptoms of migraine and a modulation of inhibitoy synaptic neurotransmission may explain this effect in our migraine patient.

Introduction In the literature there are few data about the use of pharmacological treatments (acute and prophylaxis) of primary headaches [migraine (M), tension-type headache (TTH)] in children [1]. Materials and methods Retrospective multicentre study conducted in 13 Juvenile Headache Centres; inclusion criteria: 1) diagnosis of primary headache (ICHD-II 2004); 2) stable headache pattern (>6 months). Results Seven hundred and thirty-two cases (349 m, 383 f), mean age: 12 years. Headache types: M 68%, TTH 21%, M+TTH 5%, other 4%. The statistical analysis, conducted on patients with M or TTH (n=659), considered: efficacy and safety of several drugs, any differences based on age, diagnosis and geographical distribution. Symptomatic treatment: 93% of children (M 95%, TTH 88%); type of drug: paracetamol (M 75%, TTH 75%), NSAIDs (M 51%, TTH 27%), triptans (M 6%, TTH 0%); good-excellent efficacy 72%, good-excellent tolerability 92%. Prophylaxis therapy: 52% of cases (M 45%, TTH 44%); type of drug: flunarizine (M 18%, TTH 2%), pizotifen (M 6%, TTH 0%), amitriptyline (M 3%, TTH 5%), anticonvulsants (M 7%, TTH 1%), supplements (M 31%, TTH 34%), melatonin (M 10%, TTH 10%); good-excellent efficacy 76%, good-excellent tolerability 85%. Discussion and conclusions In our study population M prevails (76%). Symptomatic therapy is frequently used (93%), more often in M than TTH, with good efficacy and tolerability for all drugs; it is ineffective only in 10% of cases (range 7-23%). The use of NSAIDs prevail in M than TTH; few M (6%) use triptans. Prophylaxis therapy, prescribed in about half of cases (both in M and TTH), is ineffective in 12% of cases, but is usually well tolerated; supplements (32%) and flunarizine (14%) prevail.

Introduction The are few data in the literature about the use of pharmacological and non-pharmacological therapies for primary headaches (migraine: M; tension-type headache: TTH) in children [1]. Materials and methods A retrospective study was conducted by twelve Juvenile Headache Centres; inclusion criteria: (1) diagnosis of primary headache (ICHD-II, 2004); (2) stable headache pattern ([6 months). Results Three hundred and twenty cases (163 M, 157 F) with mean age at interview of 11.1 ± 3.2 years (1–19 years). Headache types: M 71% (MO 62%, MA 6%, chronic M 3%), TTH 20% (ETTH 17%, CTTH 3%), and M + TTH 7%, other 2%. A) Symptomatic treatment used in 92% of cases (1 drug 57%, 2 drugs 26%, 3 drugs 9%); M 95% versus TTH 82% (p\0.0002); type of drug: paracetamol (P) (M 84%, TTH 73%), NSAIDs (M 46%, TTH 24%), triptans (T) (M 5%, TTH 0%); good–excellent efficacy 53%, good–excellent tolerability 86%. Prescriber: paediatrician (47%), child neuropsychiatry (41%), self-prescription (10%). (B) Prophylaxis therapy used in 46% of cases (1 drug 31%, 2 drugs 11%, 3 drugs 4%); M 53% versus CT 29% (p\0.01); type of drug: flunarizine (M 22% vs. TTH 2%, p\0.0002), pizotifen (M 7%, TTH 0%), propranolol (M 3%, TTH 0%), amitriptyline (M 1%, TTH 2%), anticonvulsants (M 7%, TTH 0%), supplements (M 25%, TTH 19%), melatonin (M 4%, TTH 6%); good–excellent efficacy 65%, good– excellent tolerability 80%. Prescriber: paediatrician (14%), child neuropsychiatrist (84%), no self-prescription. (C) Non-pharmacological treatments (N = 27, 8%): relaxation/biofeedback (30%), cognitive-behavioural therapy (22%), homeopathy (15%), treatment of malocclusion (15%), acupuncture (7%), psychotherapy (7%) and biofeedback (4%). (D) Rating more effective therapy: pharmacological symptomatic (57%) than prophylaxis combined with symptomatic (25%) or alone (16%); better tolerated therapy: pharmacological symptomatic (57%), than prophylaxis combined with symptomatic (22%) or alone (18%). Main expectations of the patient: effect on pain (62%), speed of action (30%) and lack of side effects (21%). Discussion and conclusions The study population consists predominantly of migraineurs (71%). The therapy most widely used was symptomatic (92%), especially P or NSAIDs, with limited use of T (E 5%) with good efficacy and tolerability. The prophylactic drugs most used were supplements (25%) and flunarizine (22%), while AEDs were rarely used (7%). The prophylaxis was ineffective in a third of migraineurs (28–34%), although often well tolerated (43–60%). The non-pharmacological therapy was not widely used (7%) and rarely preferred by patients (2–3%).

Lo scopo del presente studio è quello di esaminare le caratteristiche psicometriche di un nuovo strumento, l’Headache Specific Quality of Life (HSQoL), che misura gli effetti del mal di testa sulla qualità della vita di bambini e adolescenti che soffrono di cefalea. L’HSQoL è stato compilato da 272 soggetti che soffrono di cefalea (dai 9 ai 15 anni) e dai loro genitori, contattati presso un centro cefalee e presso delle scuole. Il HSQoL è composto da un breve questionario sulle caratteristiche del mal di testa (frequenza degli attacchi, durata, localizzazione, sintomi ad esso associati, ecc) e 4 scale (Scale di Impatto, di Evitamento, di Timori Relazionali e di Disagio Autopercepito). Tutte le scale mostrano una struttura monofattoriale e, ad eccezione della scala di timori relazionali, un soddisfacente livello di attendibilità. I punteggi HSQoL ottenuti da bambini e adolescenti permettono di differenziare tra soggetti che sono in trattamento da pazienti in prima visita. In questo studio, inoltre, è stata valutata la congruenza tra report dei genitori e report dei loro figli circa l’influenza del mal di testa sulla qualità della vita, evidenziando una maggiore congruenza per quanto riguarda gli aspetti “oggettivi” (ad esempio, il numero di attacchi nell’ultimo mese) piuttosto che per gli aspetti “soggettivi” (punteggi alla scala di Impatto). In generale, i risultati dello studio indicano che l’HSQoL , uno strumento breve e di facile somministrazione, può essere utilizzato sia in ambito clinico e che di ricerca per valutare l’impatto della cefalea sulla qualità della vita in età evolutiva.

Le relazioni fra disturbi del sonno e cefalea sono state oggetto di studi che hanno chiarito in parte i complessi meccanismi di interazione fra due patologie croniche e invalidanti che condividono substrati anatomici, fisiologici e biochimici. Scopo dello studio è stato valutare attraverso questionari le relazioni fra cefalea e fase e qualità del sonno in un'ampia popolazione non clinica di bambini. Materiale e metodo. In 4 scuole elementari e medie di Roma, è stato prima spiegato lo scopo dello studio in un incontro con genitori e insegnanti. Poi agli studenti è stata proposta una versione modificata della School Sleep Habits Survey (Wolfson & Carskadon, 1998) che comprendeva domande su pattern, abitudini e qualità del sonno e 3 scale psicometriche: 1) Sleepiness Scale; 2) Sleep-Wake Problems Behaviour Scale; 3) Morningness/eveningness scale. Inoltre è stato consegnato un questionario sulle cefalee per bambini costruito dagli Autori. I ricercatori presenti alla compilazione in classe hanno raccolto 1073 questionari completati da 546 maschi e 527 femmine, età media 10,6 anni; range 8-15; D.S 1,10 anni). I dati sono stati analizzati con analisi di cross-tabulazione e chi quadrato e con test di correlazione di Pearson. Risultati. Il 21.4% degli studenti riporta cefalea con frequenza di almeno una volta a settimana (5% tutti i giorni, 7.4% più di una volta a settimana, 9% una volta a settimana), il 16% riporta cefalea 1-2 volte al mese e il rimanente 61.5% meno di una volta al mese. Solo 31 soggetti (2.93%) hanno riferito di non avere mai sofferto di cefalea. Nel 49.3% dei soggetti che riferivano cefalea gli attacchi duravano meno di mezzora, nel 18.0% circa 1 ora, nel 4.6% circa 2, e nel 18% più di 2 ore. Gli attacchi avvenivano più spesso al mattino (25.6%) e alla sera (26.4%), meno il pomeriggio (11.1%); attacchi notturni si verificavano nel 8.3%. I motivi più frequenti attribuiti alla comparsa del mal di testa erano: sentirsi stanco o aver dormito male (31.2%), provare rabbia, tristezza o preoccupazione (21.9%). Usando un criterio di durata e frequenza (almeno 1 attacco a settimana e durata = > 1 ora) sono stati identificati 124 (11.56%) soggetti con cefalea ricorrente. Circa il 75% di essi erano serotini(E) mentre circa la metà dei soggetti senza cefalea ricorrente erano mattutini (M). Non sono emerse differenze fra i due gruppi nelle abitudini e nei pattern di sonno (ora di addormentamento, di risveglio e durata del sonno) e la scala di sonnolenza. Differenze significative sono state invece riscontrate nella Sleep-Wake Problems Behaviour Scale [F(1,1069)=8,31; prob.

Introduction. Recent studies on adults and children with migraine have revealed either cortical hyperexcitability or loss of habituation using different Erp paradigms. The aim of the present study was to investigate both phenomena by measuring different cortical responses (recorded in different experimental conditions) within the same patients. Method. Subjects were 10 children (ages 9–15 years) diagnosed as suffering from migraine without aura following the IHS criteria and 10 age-matched controls. P300 amplitudes and latencies were recorded from Fz, Cz, and Pz during a passive and an active version of acoustic oddball paradigm, while CNV and its subcomponents (iCnv, lCNV) were recorded in the same sites during the interval of 3 s between S1 and S2 in a CNV classic paradigm. Results. The migraine group displayed a significantly prolonged latency of P300, particularly during the active version of the oddball task (F(1,19) = 7.1, P = 0.02). Migrainous subjects did not differ from healthy controls in the amplitudes of P300, tCNV, iCNV and lCNV. Analyses of habituation evidenced that migrainous children showed a lower habituation than healthy controls of P300 amplitudes (F(2,38) = 5.03, P = 0.01). Discussion. Present results suggest that children suffering from migraine without aura have an increased cognitive processing time and a lower habituation of cortical responses.

Introduction. The present research is a meta-analytic review which summarizes the results of studies that have assessed information processing through ERP techniques comparing migraine subjects in the interictal period with controls. Method. Studies of potential interest (n = 133) were identified in PsycLit and MedLine databases. Sixty-five (53 conducted on adults and 12 on children and adolescents) presented valid data reporting a total of 332 effects. Different meta-analyses were conducted considering the following different experimental paradigms: Flash, Steady-State, Pattern-Reversal, Intensity dependence, CNV. A further meta-analysis was conducted for evaluating habituation effect across paradigms. Effect size indices (g, d and the equivalent r) were computed through DSTAT software and analysed following Hedges and Olkin procedures. Results. Studies consistently showed, in migraine sufferers compared with control, greater amplitudes of ERP during acoustic stimulation of increasing intensities (d = +0.73; r = 0.34, P < 0.001) and greater CNV amplitudes, particularly in the initial component of CNV (d = +0.58; r = 0.28, P < 0.001). Furthermore, a lack of habituation (d = -0.85; r = -0.39, P < 0.001) in migrainous subjects was clearly demonstrated. No difference between migraine subtypes was found. Discussion. Overall, our meta-analytic findings clearly demonstrate greater cortical reactivity in migraine subjects than in controls, as indicated by cortical hyperexcitability and lack of habituation. Results suggest that ERP recordings are useful for revealing differences in information processing between migrainous subjects and controls, but they do not contribute to differential diagnosis of migraine sub-types.

The aim of the present study is evaluating the clients' satisfaction. Our headache centre takes into account both medical and psychological aspects of headache, proposing a psycho-educative assessment, in addition to a neurological assessment.

According to the project DOW, the "Communities VREs Evaluation and Recommendations" deliverable consists of: (i) Description and assessment of the work done and (ii) validation of the infrastructure from the point of view of service and functionality. Specifically the goal is to: (a) engage in a continuous validation activity throughout the remaining project lifecycle; (b) report on VRE accomplishments and issues from the user community point of view; (c) highlight missing, incomplete and poorly implemented features from functional and non-functional perspectives; (d) assist in prioritizing development effort; (e) provide recommendations for improvement to future iterations. This document provides a description of the process, methods and tools to be used to achieve this activity.

This document reports on the DILIGENT project's dissemination activities performed during the third year and the 3-month extension of the project (months 25-39). It provides brief background information on the concepts that guide dissemination in DILIGENT and introduces both the activities performed during this period and the material and instruments produced. Furthermore future activities and foreseen actions, that relate to the project and go beyond its end, are presented

This document reports on the DILIGENT project's dissemination activities performed during the third year and the 3-month extension of the project (months 25-39). It provides brief background information on the concepts that guide dissemination in DILIGENT and introduces both the activities performed during this period and the material and instruments produced. Furthermore future activities and foreseen actions, that relate to the project and go beyond its end, are presented.